I got some Shimano SLX M670 shifters that come with removable shift indicators.
Are they really needed and what are the benefits of using them or removing them?

Thank you in advance for you input.

I always felt that your legs will tell you what gear you're in.

Some like them. Some do not. In the heat of the moment while mountain-biking I don't find it all that helpful to take my eyes off the trail to decipher which specific ring and cog that my chain sits in. So I generally take my indicators off when I have the option. But I don't sweat it too much if they are unremovable.

The tradeoff is mainly about looks. Do you like the appearance of your handlebar better with or without the indicators? That's pretty much all the issue boils down to.

My first high end drive train on a mountain bike had an XTR rapid rise derailleur and Sachs Quartz twist shifters. Because the derailleur was reverse operation, the shifter indicated the gears 1 thru 9 in reverse order. Was never an issue, because I never looked at it.

+1.

I couldn't care less what number gear I am in except for maybe when I am riding my largest cog, and when that happens I will know it without any gizmo to tell me that.

If it interferes with my shifter/brake lever positioning I'll remove them - had to do that on a SLX setup. Otherwise I don't worry about it.

They came on two of my bikes, one was XT the other is LX. I don't think about them. I never thought about taking them off. Neither bike is a weight weenie bike, so I don't care.

Don't really care either way, they can sometimes be nice to have, and do make some sense with an IGH, but they're not something I look for, or would take the time to remove.

They can interfere with other things on the bar like lockouts, drop post levers, bells and such.

I think the indicators are good to have when you first start using a multi-geared bike. They help you learn where you are within the range of gears you have. It's probably unnecessary if you only have a few gears but the more you have, the more confusing it can be, especially if you have multiple chainrings.

I ride a single speed bike now. I don't like the noise, maintenance and distraction of having a bunch of gears. Sure, you have to have them in many circumstances. But I don't live in a mountainous area. There are some 10% grade hills. But not many. I just work harder and enjoy the unencumbered joy of riding without noise and the distraction of shifting gears. Of course, I'm not setting any land speed records and every once in a while I have to get off the bike and walk it. But nothing's for free.

IGH, the shifting is linear lever has 3 positions or 1 to 14 in a row.. Derailleur bikes mine are Friction shift.

when in doubt look down at the wheel..

Ihe companies always seem to make bikes car like so more people buy new bikes to get the feature..

Gear numbered windows , more speeds etc.

Yup, It has been hard for me to embrace the dancing chain, I have ridden an old British 3 speed for years and never warmed up to the idea of so meany gears and the chain jumping around them all. It just seems a sloppy mess to me still.
In the early 70's I once said it was a passing fad.
Time has proven me wrong on that one!
But now I'm trying to do it right, sorting out the do's and don'ts.
Don't get low level parts if you want a smooth clean shift, That I have learned the hard way.

An interesting question:

I used to have a road bike and a tandem that both had Shimano Flight Deck computers with gear indicators on the computer. I really liked it on the tandem because I couldn't just look down to tell what gear I was in but pretty much just ignired them on the single road bike.

I ride recumbents today and again find myself unable to look back at my cassette to see what gear I'm in. One had index shifting so I can pretty well tell by looking at the shifter. The other has a friction shifter. I sometimes find myself wondering whether or not I'm in my biggest rear cog.

like the 100 years war between them IGH were English, Derailleurs were so French..

I personally like to know what gear I'm in. On routes like my commute where I use the same gears in the same places with a few variations, I like to know what gear I'm in and how many shifts to make to get to where I want to be. My utility and gravel bikes both have indicators and I use them. My road bike with 105-5700 does not have indicators, and I typically keep a mental note of what gear I'm in. But sometimes I forget and just look down. Other times I think I'm in a certain gear, but I'm actually in the next one higher or lower.

I have the same shifters you have, and I kept the indicators on.
I don't have much use for the cog indicator, but the chainring indicator is one I reference.
There is so much over lap between the ratios that I can "think" I'm in the large ring when in fact I'm in the small.
A quick glance tells me what I need to know.

I have a pair of XTR triggers, no indicators, none wanted.

Just about you like it or not

On my recreational bike they broke and I decided not to fix them. I just got a new shifter for my commuter. I pretty much stay in one gear, but I do use it.

That's my experience too. Gear indicators are very helpful on a tandem.